As is well known in the art, an optical Fourier transformation can be performed on a subject by illuminating the subject with a coherent light source and using a lens to collect the reflected, and/or diffracted and/or transmitted light containing optical information corresponding to the subject. The lens will define a Fourier transform of the orignal subject information in a plane located one focal length away from the lens at its focus. With this process, subject information is redistributed in the Fourier transform plane to correspond to spatial frequency content. A second lens, located two focal lengths from the first, images the information onto a display screen, recording medium, or the like.
The optical information coming from the subject may be manipulated for the purpose of enhancing detail, removing unwanted subject information, isolating defects, or making precise topographic and optical path measurements. This is accomplished by blocking a portion of the subject information or changing its phase within the transform plane. These techniques are particularly useful where the subject consists of repetitive spatial frequency content such as is present in photomasks or wafers used in the production of microelectronic circuits, since the optical Fourier transform will consist of an array of regularly spaced points of light whose distance from the optical axis is proportional to the spatial frequency.
One example of such a technique is disclosed in U.S. Pat. No 4,000,949 issued Jan. 4, 1977 to Watkins. Using the basic processing scheme outlined above, a photomask is used as the subject. An optical spatial filter is placed within the Fourier transform plane for blocking all subject information other than that corresponding to nonperiodic defects in the mask. Since only defect information will pass through to the display screen, the number of defects and their locations can be determined.
It can be easily seen, however, that aberrations within the optical components of an optical processor, particularly within lenses focusing the subject information and/or the processed information, will be a significant detriment to use of the otpical processor with subjects having microscopic detail. On axis, for example, a focus error aberration can cause loss of spatial frequency information, as illustrated by way of example for a typical optical telescope system in FIG. 1.
A three-lens system 24 is shown, wherein lenses 1.sub.1 and 1.sub.2 are F/1.50, 50 mm diameter, 75 mm focal length lenses, and lens 1.sub.3 is an F/1.50, 150 mm diameter, 225 mm focal length lens. Assuming the sum of the spherical aberration from lenses 1.sub.2 and 1.sub.3 to be 2 mm, the focus of the rays 26 entering the system 24 is moved from a point 28 to a point 30, 77 mm away from lens 1.sub.1. This results in a smaller, F/1.54 collection angle at lens 1.sub.1.
Therefore, with a 225 mm focal length for lens 1.sub.3, which would give an F/4.5 collection angle for lens 1.sub.3 and the system 24 as a whole if lens 1.sub.1 collected F/1.50, the lens can only collect: ##EQU1##
Similarly, for 1 mm of special aberration, the focal point is moved to 76 mm away from lens 1.sub.1 and: ##EQU2## for the system 24.
To consider these effects directly, the optical transfer function (OTF) of the system may be looked to.
For a diffraction limited system: ##EQU3## where a (f.sub.x,f.sub.y) is the area of overlap of the pupil collecting spatial frequencies with the restricting pupil function. The OTF with aberrations for two pupils given by: ##EQU4## where W is the aberration function.
The Schwarz inequality, EQU .vertline..intg..intg.X Y d.xi.d.eta..vertline..sup.2 .ltoreq.(.intg..intg..vertline.X.vertline..sup.2 d.xi.d.eta.) (.intg..intg..vertline.Y.vertline..sup.2 d.xi.d.eta.)
can be used to show directly that EQU H'(f.sub.x, f.sub.y).sub.aber. .vertline..sup.2 .ltoreq..vertline.H (f.sub.x,f.sub.y).sub.no abberrations .vertline..sup.2
This means that aberrations never increase the MTF (the modulus of the OTF), but rather lower the contrast of each spatial frequency component. Thus, the cutoff to the spatial frequency passed by the system will be effectively decreased and the effective F-number thereof will increase. This is especially important if there is a random background to further decrease the contrast.
Off-axis, spatial frequency information can be lost even in an ideal aberration-free system directly due to vignetting, as shown in FIGS. 2 and 3. Again, considering the sample three-lens optical system 24, the limit of the system 24 is found by tracing rays from the edge of lens 1.sub.1. The angle of incidence of these rays at a point on the subject plane 34 gives the cone angle of spatial frequency information which can be collected from that point on the subject.
In FIG. 2, using a thin lens ray trace, it can be seen that only an F/9 cone can be collected by system 24 from a point 36 located 37.5 mm off the axis 37. In FIG. 3, a point 38 located 50 mm off the axis 37 is considered. Again using a thin lens ray trace, it can be seen that only an F/13.5 cone can be collected due to vignetting.
In order to utilize optical processing techniques on objects having microscopic detail with an optical system such as is used in Watkins, it is necessary to employ within the system opitical components of very high quality. Such components will then minimize aberrations within the system. Additionally, to avoid loss of information due to vignetting, system apertures must be made as large as possible. Unfortunately, large aperture optical components of very high quality, particularly lenses, can be obtained only at extremely high cost, making optical processing for such objects far less practical.
Use of high quality lenses creates additional complications other than cost where high-resolution records are desired, since as the resolution of an imaging optic is increased, the depth of focus thereof decreases. Thus, the depth of focus available in the image plane is limited.
Full-field documentation with relatively high resolution can be accomplished through holography. By holographically recording a subject, and then reconstructing the holographic image with the conjugate to the reference beam, a three-dimensional real image of the object is created in space. This real image can then be examined microscopically as if it were the original illuminated object. An added advantage is that a holographic system can document not only reflecting surfaces but also the microstructure inside a thick, transparent object such as optical components. Since the holographic image has no substance, a microscope can focus through the image, even to the opposite side if desired, without the need for a long focus and high quality objective required when a solid object is in the way.
Examples of previous work in holographic microscopy are disclosed in Leith and Upatnieks, "Microscopy by Wavefront Reconstruction," 55 J. Opt. Soc. Amer. 569 (1965); Toth and Collins, "Reconstruction of a Three-Dimensional Microscope Sample Using Holographic Techniques," 13 Appl. Phys. Letters 7 (1968); and Briones, Heflinger and Wuerker, "Holographic Microscopy," 17 Appl. Optics 1944 (1978). The records produced are large aperture wide field of view, large depth of field, three-dimensional images of both transmitting volumes and specularly or diffuse reflecting subjects. Such work, however, has not as yet obtained both the necessary resolution and field of view for viewing and/or analyzing the microstructure of large object surface areas.
One technique available in holography, described in Toth and Collins, is known as reverse ray-tracing. When a hologram 10 is made of a subject 12 through a lens 14 or other optical components, the image information 16 from the subject may be aberrated by the lens 14 (FIG. 4a). If the hologram 10 is repositioned accurately with respect to the lens 14, and the conjugate to the reference beam 18, i.e., the same wavefront as the reference beam but travelling in the opposite direction, is used to reconstruct the holographic image, the image rays 20 will exactly retrace the path of the original subject rays back through the optical system (Fig. 4b). This is not the same as merely turning the lens 14 around, since the information about the lens aberration is stored in the hologram 10. Therefore, the aberrations of the lens 14 will be completely compensated for upon reconstruction and the holographic image 22 will be diffraction limited.
It can be seen that to produce a high resolution holographic image 22, it is not necessary to use a high quality lens 14. Thus, it would appear promising to attempt to incorporate the holographic reverse ray-trace technique into an optical processing system.
What is needed, therefore, is a method and apparatus for optical processing that utilizes holography, and specifically the reverse ray-tracing technique. Such a method and apparatus would enable optical processing to be performed on both detailed three-dimension microscopic and macroscopic subjects with high resolution.